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Full-Text Articles in Physical Sciences and Mathematics
Quantum States Localized On Lagrangian Submanifolds, François Ziegler
Quantum States Localized On Lagrangian Submanifolds, François Ziegler
Department of Mathematical Sciences Faculty Presentations
Let X be a symplectic manifold and Aut(L) the automorphism group of a Kostant-Souriau line bundle on X. *Quantum states for X*, as defined by J.-M. Souriau in the 1990s, are certain positive-definite functions on Aut(L) or, less ambitiously, on any “large enough” subgroup G of Aut(L). This definition has two major drawbacks: when G = Aut(L) there are no known examples; and when G is a Lie subgroup the notion is far from selective enough. In this talk I’ll introduce the concept of a quantum state *localized at Y *, where Y is a coadjoint orbit of a subgroup …
Eigenvalue Estimates Of Laplacians Defined By Fractal Measures, Sze-Man Ngai
Eigenvalue Estimates Of Laplacians Defined By Fractal Measures, Sze-Man Ngai
Department of Mathematical Sciences Faculty Presentations
We study various lower and upper estimates for the first eigenvalue of Dirichlet Laplacians defined by positive Borel measures on bounded open subsets of Euclidean spaces. These Laplacians and the corresponding eigenvalue estimates differ from classical ones in that the defining measures can be singular. By using properties of self-similar measures, such as Strichartz's second-order self-similar identities, we improve some of the eigenvalue estimates.